When a system of equations Ax = b has at least one solution, we say that the system is consistent, otherwise inconsistent. We are concerned with determining when a system of equations is consistent and studying the number of solutions of a system of equations. After having learned the theory of linear algebra, one can observe that the existence (of at least one) and the uniqueness of solutions ...

in this paper, we show that a matrix a in mn(c) that has n coneigenvectors, where coneigenvaluesassociated with them are distinct, is condiagonalizable. and also show that if allconeigenvalues of conjugate-normal matrix a be real, then it is symmetric.

Abstract. Many real processes can be modeled by stochastic differential equations with aftereffect [1]-[3]. Stability conditions for such systems can be obtained by construction of appropriate Lyapunov functionals using special procedure of Lyapunov functionals construction [4]-[14]. In this paper asymptotic mean square stability of stochastic linear differential equations with discrete and dis...

Cauchy’s theorem is used to generate a Complex Variable Boundary Element Method (CVBEM) formulation for steady, two-dimensional potential problems. CVBEM uses the complex potential, w"/#it, to combine the potential function, /, with the stream function, t. The CVBEM formulation, using Cauchy’s theorem, is shown to be mathematically equivalent to Real Variable BEM which employs Green’s second id...

Loop equations of matrix models express the invariance of the models under field redefinitions. We use loop equations to prove that it is possible to define continuum times for the generic hermitian 1-matrix model such that all correlation functions in the double scaling limit agree with the corresponding correlation functions of the Kontsevich model expressed in terms of kdV times. In addition...

We derive bounds on the variance of a finite universe. Some related inequalities for the roots of the polynomial equations and bounds for the largest and smallest eigenvalues of a square matrix with real spectrum are obtained.

The article focuses on the linear estimation problems of unknown rectangular matrices, which are solutions matrix equations with right-hand sides belonging to bounded sets. random errors observation vector have zero mathematical expectation, and correlation is belongs one two Explicit expressions guaranteed root mean square estimates for operators acting from space matrices into some given. Gua...

GMRES is a popular iterative method for the solution of large linear systems of equations with a square nonsingular matrix. When the matrix is singular, GMRES may break down before an acceptable approximate solution has been determined. This paper discusses properties of GMRES solutions at breakdown and presents a modification of GMRES to overcome the breakdown.